TALKING ABOUT PROBABILITIES: A LOGICAL PROBLEM FOR OR/MS

The correct interpretation of a natural language statement is determined as much by convention and shared meanings as by logical content. Therefore, when the word “probability” is used in the statement of a decision problem, the intended interpretation is not always clear. If such a statement also contains explicit probability formulae, confusion and even paradox may result. In this article, a problem involving cascaded inference is interpreted in four ways, three of which are regarded by the authors as legitimate or reasonable. The problem was originally suggested by Einhorn [3] and further discussed by Libby [10]. It is suggested here that a formal, mathematicist interpretation of the word “probability” might lead to inappropriate analyses of some decisions.     

Determining the minimum duration of treatment in tuberculosis: An order restricted non-inferiority trial design

Tuberculosis (TB) is one of the biggest killers among infectious diseases worldwide. Together with the identification of drugs that can provide benefits to patients, the challenge in TB is also the optimisation of the duration of these treatments. While conventional duration of treatment in TB is 6 months, there is evidence that shorter durations might be as effective but could be associated with fewer side effects and may be associated with better adherence. Based on a recent proposal of an adaptive order-restricted superiority design that employs the ordering assumptions within various duration of the same drug, we propose a non-inferiority (typically used in TB trials) adaptive design that effectively uses the order assumption. Together with the general construction of the hypothesis testing and expression for type I and type II errors, we focus on how the novel design was proposed for a TB trial concept. We consider a number of practical aspects such as choice of the design parameters, randomisation ratios, and timings of the interim analyses, and how these were discussed with the clinical team.     

Within- and between-person associations among internalizing and externalizing problems during middle childhood

Internalizing and externalizing problems are likely to co-occur in childhood and are related to concurrent and prospective mental health outcomes. We examined the longitudinal relations among internalizing and externalizing problems during middle childhood utilizing the Random Intercept – Cross Lagged Panel Model. We investigated three research questions: (1) how overall levels of internalizing and externalizing problems are related, (2) whether internalizing and externalizing problems predict each other longitudinally, and (3) whether girls and boys show different longitudinal associations among internalizing and externalizing problems. Mother-reported internalizing and externalizing problems were used through first to sixth grade (N = 1364). Results showed positive random intercepts and positive within-time correlations of internalizing and externalizing problems. Further, internalizing problems predicted externalizing problems at the within-person level. Although previous research mostly has shown a significant effect from externalizing problems to internalizing problems, the current study shows that when within- and between-person variance are disentangled, internalizing problems also may predict externalizing problems.     

Clocks and Trees: Isomorphic Dutch Auctions and Centipede Games

We report an experiment on effects of varying institutional format and dynamic structure of centipede games and Dutch auctions. Centipede games with a clock format unravel, as predicted by theory but not reported in previous literature on two‐player tree‐format centipede games. Dutch auctions with a tree format produce bids close to risk neutral Nash equilibrium bids, unlike previous literature on clock‐format Dutch auctions. Our data provide a new, expanded set of stylized facts which may provide a foundation for unified modeling of play in a class of games that includes centipede games and Dutch auctions.